Proyecto HousePrices :P

Librerías

library(dplyr)
library(ggplot2)
library(cleandata)
library(corrplot)
library(gridExtra)
library(Metrics)
library(caret)
library(MASS)
library(robustbase)
library(cvTools)
library(sp)
library(rgdal)
library(geosphere)
library(dismo)
library(rgeos)
library(RANN)

Pre-procesamiento, limpieza y análisis inicial

median_house_value_scale = 100000

initialPreprocessing<-function(df) {
  df$ocean_proximity<-as.factor(df$ocean_proximity)
  
  op_order<-c("INLAND", "<1H OCEAN", "NEAR OCEAN","NEAR BAY", "ISLAND")
  enc_ocean_proximity<-encode_ordinal(data.frame(enc_ocean_proximity=df[["ocean_proximity"]]), order=op_order, out.int=T, full_print = F)
  df<-cbind(df, enc_ocean_proximity=enc_ocean_proximity)
  
  if("median_house_value" %in% colnames(df)) {
      df$median_house_value<-df$median_house_value / median_house_value_scale
  }
  
  return(df)
}

loadAndPreprocess<-function(csvName) {
  return(initialPreprocessing(read.csv(csvName)))
}

all_data=loadAndPreprocess("train.csv")

coded 1 cols 5 levels 

all_data

Es bastante claro que al menos en cierta medida, la proximidad al océano afecta el precio. Esto nos da una pista de que podemos codificar esta variable como ordinal. Movimos esto a nuestra función de pre-procesamiento arriba para aprovecharlo en cualquier dataset.

all_data %>% 
  group_by(ocean_proximity) %>%
  summarize(mean_value = mean(median_house_value)) %>%
  arrange(desc(mean_value))

Usamos summary para ver cuáles columnas tienen NAs y verificamos el valor mínimo de cada columna para asegurarnos que no hay NAs disfrazados de 0

summary(all_data)

Solamente total_bedrooms tiene faltantes y son 144, veamos cuánto es eso en porcentaje.

naCount<-sum(is.na(all_data$total_bedrooms))

naCount / length(all_data$total_bedrooms) * 100

Prácticamente 1% de datos faltantes. Nos ocuparemos de ellos, pero antes debemos divir los datos en train/test

set.seed(279720)
spec = c(train = .80, validate = .20)
#spec = c(train = .7, test = .15, validate = .15)

g = sample(cut(
  seq(nrow(all_data)), 
  nrow(all_data)*cumsum(c(0,spec)),
  labels = names(spec)
))

data = split(all_data, g)

nasRemoved<-data$train %>% 
  dplyr::select(-c(ocean_proximity, id)) %>%
  filter(!is.na(total_bedrooms))
         
corrplot(cor(nasRemoved), 
         method = "ellipse", 
         type="full",
        addCoef.col = rgb(0,0,0, alpha = 0.6), diag = TRUE, number.cex=0.77, 
        col= colorRampPalette(c("red","white", "green"))(100))

Imputación

Vemos que nuestra variable con NAs (total_bedrooms) tiene correlación casi perfecta con households, por lo que usaremos el valor de esta para obtener datos de imputación.

imp_total_bedrooms<-function(df, traindata=nasRemoved) {
  x<-traindata$households
  y<-traindata$total_bedrooms
  lr<-lm(y ~ x)
  new<-data.frame(x = df$households)
  
  df$total_bedrooms<-as.integer(ifelse(is.na(df$total_bedrooms), 
                                predict(lr, new), 
                                df$total_bedrooms))
  
  return(df)
}

data$train<-imp_total_bedrooms(data$train)
data$validate<-imp_total_bedrooms(data$validate)

print(summary(data$train$total_bedrooms))

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    2.0   296.0   435.0   534.9   642.0  6445.0 

print(summary(data$validate$total_bedrooms))

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    3.0   297.0   439.0   542.7   658.8  4492.0 

Outliers pt.1

plot_outliers<-function(df, colname) {
  column<-sym(colname)

  hist<-ggplot(df, aes(x=!!column))+
    geom_histogram(color="white", fill="blue")+
    theme_minimal()
  
  box<-ggplot(df, aes(x=!!column))+
    geom_boxplot()+
    theme_minimal()
  
  
  qq<-ggplot(df, aes(sample=!!column))+
    stat_qq()+
    stat_qq_line(col="red", lwd=1)
    theme_minimal()

  grid.arrange(hist, box, qq, ncol=3)
}

plotAllOutliers<-function(data) {
  filtered<-data
  if("id" %in% colnames(data)) {
    filtered<-data %>% 
        dplyr::select(-c(ocean_proximity, id)) %>%
        filter(!is.na(total_bedrooms))
  }
  for (col in names(filtered)) {
     plot_outliers(filtered, col)
  }
}

plotAllOutliers(data$train)

Creación y análisis de nuevos features

beds_per_rooms<-data$train$total_bedrooms / data$train$total_rooms
rooms_per_household<-data$train$total_rooms / data$train$households
income_per_capita<-data$train$median_income/data$train$population
income_per_household<-data$train$median_income/data$train$households
beds_per_capita<-data$train$total_bedrooms / data$train$population
rooms_per_capita<-data$train$total_rooms / data$train$population
pop_per_household<-data$train$population/data$train$households # check this one agian after doing something with the outliers
pop_per_bedroom<-data$train$population/data$train$total_bedrooms
pop_per_room<-data$train$population/data$train$total_rooms

candidates<-data.frame(beds_per_rooms, rooms_per_household, income_per_capita, income_per_household, beds_per_capita, rooms_per_capita, pop_per_household, pop_per_bedroom, pop_per_room, data$train$median_house_value)

summary(candidates)
corrplot(cor(candidates), 
         method = "ellipse", 
         type="full",
        addCoef.col = rgb(0,0,0, alpha = 0.6), diag = TRUE, number.cex=0.7,  tl.cex=0.75 , 
        col= colorRampPalette(c("red","white", "green"))(100))

addExtraFeats<-function(df) {
  if("beds_per_rooms" %in% colnames(df)) { 
    return(df)
  }
  
  beds_per_rooms<-df$total_bedrooms / df$total_rooms
  rooms_per_household<-df$total_rooms / df$households
  income_per_capita<-df$median_income/df$population
  income_per_household<-df$median_income/df$households
  beds_per_capita<-df$total_bedrooms / df$population
  rooms_per_capita<-df$total_rooms / df$population
  pop_per_household<-df$population/df$households  
  
  return(cbind(df, beds_per_rooms, rooms_per_capita, rooms_per_household, income_per_capita))
}

data$train<-addExtraFeats(data$train)
data$validate<-addExtraFeats(data$validate)

Entrenamiento de modelo pt.1

model_rmse<-function(model, observations, actual_values, scale=median_house_value_scale) {
  predictions<-predict(model, observations)
  return(rmse(predictions, actual_values)*scale)
}

scores<-function(model, xs=data$validate, y=data$validate$median_house_value, cost = rmspe, ...) {
  folds <- cvFolds(nrow(xs), K = 5, R = 10)
  return(data.frame(
    validation_error=model_rmse(model, xs, y),
    k_fold_cv_error=repCV(model, cost = cost, folds = folds, ...)$cv[[1]]*median_house_value_scale
  ))
}

extractTrainingVars<-function(data) {
  return(data %>% dplyr::select(median_house_value, 
                median_income,
                enc_ocean_proximity,
                total_rooms,
                latitude,
                longitude,
                total_bedrooms,
                housing_median_age,
                beds_per_rooms,
                rooms_per_capita,
                rooms_per_household,
                population,
                income_per_capita))
}

training_vars_1<-extractTrainingVars(data$train)

fit1<-lm(median_house_value ~ ., data = training_vars_1)
scores(fit1)

NA

Outliers pt.2

plots

outlier_values <- boxplot.stats(data$train$total_rooms)$out  # outlier values.
boxplot(data$train$total_rooms, main="total_rooms", boxwex=0.1)
print(outlier_values)

outlier_values <- boxplot.stats(data$train$total_bedrooms)$out  # outlier values.
boxplot(data$train$total_bedrooms, main="total_bedrooms", boxwex=0.1)
print(outlier_values)

outlier_values <- boxplot.stats(data$train$population)$out  # outlier values.
boxplot(data$train$population, main="population", boxwex=0.1)
print(outlier_values)

outlier_values <- boxplot.stats(data$train$households)$out  # outlier values.
boxplot(data$train$households, main="households", boxwex=0.1)
print(outlier_values)

outlier_values <- boxplot.stats(data$train$median_income)$out  # outlier values.
boxplot(data$train$median_income, main="median_income", boxwex=0.1)
print(outlier_values)

outlier_values <- boxplot.stats(data$train$median_house_value)$out  # outlier values.
boxplot(data$train$median_house_value, main="median_house_value", boxwex=0.1)
print(outlier_values)

Cook’s distance

cooksd<-cooks.distance(fit1)
plot(cooksd, pch="*", cex=1, main="Influential Obs by Cooks distance")  # plot cook's distance
abline(h = 4*mean(cooksd, na.rm=T), col="red")  # add cutoff line

text(x=1:length(cooksd)+1, y=cooksd, labels=ifelse(cooksd>4*mean(cooksd, na.rm=T),names(cooksd),""), col="red")  # add labels

Eliminación de los peores outliers

distances<-data.frame(d=cooksd[cooksd>4*mean(cooksd, na.rm=T)])
distances<-distances %>% arrange(desc(d))
indices<-as.integer(row.names(distances))

removeTopNOutliers<-function(n, indices, data) {
  return( data[-match(indices[1:n], rownames(data)), ])
}

trainMinusTopOL<-removeTopNOutliers(3, indices, data$train)
trainMinusAllOL<-removeTopNOutliers(length(indices), indices, data$train)
fitTop3  <-lm(median_house_value ~ ., data = extractTrainingVars(trainMinusTopOL))
fitAll<-lm(median_house_value ~ ., data = extractTrainingVars(trainMinusAllOL))
scores(fitTop3  )

scores(fitAll)

data$train[match(indices[1:3], rownames(data$train)),]

summary(fitTop3)

Call:
lm(formula = median_house_value ~ ., data = extractTrainingVars(trainMinusTopOL))

Residuals:
    Min      1Q  Median      3Q     Max 
-3.8735 -0.3926 -0.0798  0.2980  4.9730 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)         -3.214e+01  1.046e+00 -30.727  < 2e-16 ***
median_income        4.280e-01  4.786e-03  89.444  < 2e-16 ***
enc_ocean_proximity  4.394e-02  9.341e-03   4.704 2.59e-06 ***
total_rooms         -2.998e-06  1.222e-05  -0.245  0.80621    
latitude            -3.857e-01  1.099e-02 -35.089  < 2e-16 ***
longitude           -3.789e-01  1.196e-02 -31.678  < 2e-16 ***
total_bedrooms       2.456e-04  6.557e-05   3.746  0.00018 ***
housing_median_age   1.027e-02  5.601e-04  18.330  < 2e-16 ***
beds_per_rooms       2.210e+00  1.723e-01  12.830  < 2e-16 ***
rooms_per_capita     5.535e-01  1.868e-02  29.624  < 2e-16 ***
rooms_per_household -1.840e-01  7.941e-03 -23.168  < 2e-16 ***
population          -4.976e-05  1.703e-05  -2.922  0.00349 ** 
income_per_capita   -1.869e+00  3.962e-01  -4.717 2.42e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6592 on 11541 degrees of freedom
Multiple R-squared:  0.6782,    Adjusted R-squared:  0.6779 
F-statistic:  2027 on 12 and 11541 DF,  p-value: < 2.2e-16

summary(fitAll)

Call:
lm(formula = median_house_value ~ ., data = extractTrainingVars(trainMinusAllOL))

Residuals:
     Min       1Q   Median       3Q      Max 
-2.48273 -0.38226 -0.06987  0.30022  3.09619 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)         -3.104e+01  9.980e-01 -31.097  < 2e-16 ***
median_income        4.726e-01  5.029e-03  93.980  < 2e-16 ***
enc_ocean_proximity  2.629e-02  8.812e-03   2.984  0.00285 ** 
total_rooms         -2.486e-05  1.279e-05  -1.943  0.05201 .  
latitude            -3.654e-01  1.051e-02 -34.753  < 2e-16 ***
longitude           -3.598e-01  1.140e-02 -31.555  < 2e-16 ***
total_bedrooms       2.889e-04  6.983e-05   4.138 3.54e-05 ***
housing_median_age   1.219e-02  5.333e-04  22.867  < 2e-16 ***
beds_per_rooms       3.004e+00  1.883e-01  15.952  < 2e-16 ***
rooms_per_capita     6.237e-01  2.023e-02  30.837  < 2e-16 ***
rooms_per_household -1.917e-01  8.342e-03 -22.976  < 2e-16 ***
population          -1.959e-05  1.951e-05  -1.004  0.31532    
income_per_capita   -3.863e+00  8.563e-01  -4.511 6.51e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6168 on 11418 degrees of freedom
Multiple R-squared:  0.7102,    Adjusted R-squared:  0.7099 
F-statistic:  2332 on 12 and 11418 DF,  p-value: < 2.2e-16

Outliers test

outlierIndices<-as.numeric(names(car::outlierTest(fit1)[[1]]))
trainMinusAllOL2<-removeTopNOutliers(length(outlierIndices), outlierIndices, data$train)
fitAll2<-lm(median_house_value ~ ., data = extractTrainingVars(trainMinusAllOL2))
scores(fitAll2)

Capping

candidates<-data.frame(
  original=data_train$total_rooms,
  cap_default=cap(data_train$total_rooms)
  ,cap_5=cap(data_train$total_rooms, IQR_factor = 19)


)

plotAllOutliers(candidates)
compare_capped_performance(data_train, "total_rooms", candidates)

candidates<-data.frame(
  original=data_train$total_bedrooms,
  cap_default=cap(data_train$total_bedrooms)
    ,cap_2=cap(data_train$total_bedrooms, IQR_factor = 1.5)
  ,cap_3=cap(data_train$total_bedrooms, IQR_factor = 2)
  ,cap_5=cap(data_train$total_bedrooms, IQR_factor = 7)
  ,cap_5=cap(data_train$total_bedrooms, IQR_factor = 16)


)

plotAllOutliers(candidates)
compare_capped_performance(data_train, "total_bedrooms", candidates)

candidates<-data.frame(
  original=data_train$population,
  cap_default=cap(data_train$population)
  ,cap_6=cap(data_train$population, IQR_factor = 18)


)

plotAllOutliers(candidates)
compare_capped_performance(data_train, "population", candidates)

candidates<-data.frame(
  original=data_train$households,
  cap_default=cap(data_train$households)
  ,cap_2=cap(data_train$households, IQR_factor = 1.5)
  ,cap_6=cap(data_train$households, IQR_factor = 17.5)

)

plotAllOutliers(candidates)
compare_capped_performance(data_train, "households", candidates)

candidates<-data.frame(
  original=data_train$median_income,
  cap_default=cap(data_train$median_income)
  ,cap_2=cap(data_train$median_income, IQR_factor = 1.5)
  ,cap_3=cap(data_train$median_income, IQR_factor = 2) ##DING!
)

[1] "caps: 1.59103 7.359005"
[1] "thresholds: -0.721837500000001 8.0524625"
[1] "caps: 1.59103 7.359005"
[1] "thresholds: -0.721837500000001 8.0524625"
[1] "caps: 1.59103 7.359005"
[1] "thresholds: -1.818625 9.14925"

#plotAllOutliers(candidates)
compare_capped_performance(data_train, "median_income", candidates, extract = extractTrainingVars)

[1] "original"
[1] "66916.2373841967" "65258.6203328887"
[1] "cap_default"
[1] "68736.2718041317" "65228.7634702003"
[1] "cap_2"
[1] "68736.2718041317" "65239.9032777355"
[1] "cap_3"
[1] "68265.5792341056" "65022.490643416" 

compare_capped_performance(data_train, "median_income", candidates)

[1] "original"
[1] "66899.9244852506" "65236.6103980749"
[1] "cap_default"
[1] "68665.1343300481" "65213.0030072346"
[1] "cap_2"
[1] "68665.1343300481" "65214.9882612058"
[1] "cap_3"
[1] "68195.6474577282" "65005.7533989622"

prueba<-data_train
prueba[["median_income"]]<-candidates$cap_3

fit_cap<-lm(median_house_value ~ ., data = extractAndRecalculateTrainingVars(prueba))
scores(fit_cap)

Transformaciones y escalado

preProcess1<-preProcess(subset(data_train, select=-c(median_house_value, latitude, longitude, id)))
train1<-predict(preProcess1, data_train)
validate1<-predict(preProcess1, data$validate)

preProcess1<-preProcess(subset(data_train, select=-c(median_house_value, latitude, longitude, id)))
train1<-predict(preProcess1, data_train)
validate1<-predict(preProcess1, data$validate)

fitpp2<-lm(median_house_value ~ median_income+poly(median_income, 2) +
                                latitude * longitude +
                                enc_ocean_proximity +
                                population+poly(population, 2)+
                                total_rooms*total_bedrooms+
                                total_bedrooms+poly(total_bedrooms, 3)+
                                housing_median_age+poly(housing_median_age, 3)+
                                beds_per_rooms+poly(beds_per_rooms, 3)+
                                rooms_per_capita+
                                rooms_per_household+poly(rooms_per_household, 3)+
                                income_per_capita
                                , data = extractTrainingVars(train1))

summary(fitpp2)

Call:
lm(formula = median_house_value ~ median_income + poly(median_income, 
    2) + latitude * longitude + enc_ocean_proximity + population + 
    poly(population, 2) + total_rooms * total_bedrooms + total_bedrooms + 
    poly(total_bedrooms, 3) + housing_median_age + poly(housing_median_age, 
    3) + beds_per_rooms + poly(beds_per_rooms, 3) + rooms_per_capita + 
    rooms_per_household + poly(rooms_per_household, 3) + income_per_capita, 
    data = extractTrainingVars(train1))

Residuals:
    Min      1Q  Median      3Q     Max 
-3.5412 -0.3975 -0.0751  0.3065  5.0297 

Coefficients: (6 not defined because of singularities)
                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                   -96.888328   9.864448  -9.822  < 2e-16 ***
median_income                   0.806447   0.011196  72.031  < 2e-16 ***
poly(median_income, 2)1               NA         NA      NA       NA    
poly(median_income, 2)2        -9.211385   0.720914 -12.777  < 2e-16 ***
latitude                        1.599060   0.286084   5.589 2.33e-08 ***
longitude                      -0.933070   0.081789 -11.408  < 2e-16 ***
enc_ocean_proximity             0.054074   0.009473   5.708 1.17e-08 ***
population                     -0.040610   0.021237  -1.912 0.055878 .  
poly(population, 2)1                  NA         NA      NA       NA    
poly(population, 2)2            2.187558   1.205663   1.814 0.069642 .  
total_rooms                    -0.039359   0.044417  -0.886 0.375576    
total_bedrooms                  0.105353   0.030696   3.432 0.000601 ***
poly(total_bedrooms, 3)1              NA         NA      NA       NA    
poly(total_bedrooms, 3)2       -5.820900   3.066821  -1.898 0.057718 .  
poly(total_bedrooms, 3)3        1.201049   0.739795   1.623 0.104512    
housing_median_age              0.145205   0.007093  20.471  < 2e-16 ***
poly(housing_median_age, 3)1          NA         NA      NA       NA    
poly(housing_median_age, 3)2    1.505512   0.672137   2.240 0.025117 *  
poly(housing_median_age, 3)3    2.694581   0.667072   4.039 5.39e-05 ***
beds_per_rooms                  0.206483   0.017256  11.966  < 2e-16 ***
poly(beds_per_rooms, 3)1              NA         NA      NA       NA    
poly(beds_per_rooms, 3)2       -1.696288   0.948529  -1.788 0.073748 .  
poly(beds_per_rooms, 3)3       -5.406387   0.745723  -7.250 4.44e-13 ***
rooms_per_capita                0.487469   0.019043  25.599  < 2e-16 ***
rooms_per_household            -0.320506   0.017479 -18.336  < 2e-16 ***
poly(rooms_per_household, 3)1         NA         NA      NA       NA    
poly(rooms_per_household, 3)2  -8.357469   1.040492  -8.032 1.05e-15 ***
poly(rooms_per_household, 3)3   3.850034   0.854482   4.506 6.68e-06 ***
income_per_capita              -0.014765   0.006615  -2.232 0.025622 *  
latitude:longitude              0.016318   0.002357   6.923 4.66e-12 ***
total_rooms:total_bedrooms      0.003357   0.007667   0.438 0.661451    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6486 on 11529 degrees of freedom
Multiple R-squared:  0.6888,    Adjusted R-squared:  0.6882 
F-statistic:  1063 on 24 and 11529 DF,  p-value: < 2.2e-16

scores(fitpp2, xs=validate1, y=validate1$median_house_value)

prediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleading

66204.42 64151.6 66085.98 64009.12
65934.67 64135.29
65891.08 64631.93
65805.51 64390.26
65794.3 64320.67
65786.1 64297.81

full_threeway_model = lm(median_house_value ~ (.)^3, data = extractTrainingVars(train1))
summary(full_threeway_model)

Call:
lm(formula = median_house_value ~ (.)^3, data = extractTrainingVars(train1))

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2030 -0.3168 -0.0579  0.2401  4.1918 

Coefficients: (37 not defined because of singularities)
                                                             Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                -1.072e+02  2.342e+01  -4.575 4.80e-06 ***
median_income                                              -4.859e+01  2.437e+01  -1.994 0.046171 *  
enc_ocean_proximity                                        -1.447e+02  1.206e+01 -11.996  < 2e-16 ***
total_rooms                                                -1.379e+02  7.745e+01  -1.780 0.075044 .  
latitude                                                    1.803e+00  4.521e-01   3.989 6.67e-05 ***
longitude                                                  -1.040e+00  2.420e-01  -4.298 1.74e-05 ***
total_bedrooms                                              3.879e+01  8.719e+01   0.445 0.656422    
housing_median_age                                          5.839e+01  1.192e+01   4.896 9.90e-07 ***
beds_per_rooms                                             -1.129e+02  2.571e+01  -4.389 1.15e-05 ***
rooms_per_capita                                            4.789e+01  3.516e+01   1.362 0.173215    
rooms_per_household                                        -4.133e+01  3.135e+01  -1.319 0.187323    
population                                                  1.254e+02  4.758e+01   2.636 0.008412 ** 
income_per_capita                                           3.285e+01  1.551e+02   0.212 0.832297    
median_income:enc_ocean_proximity                          -6.423e+00  2.261e+00  -2.840 0.004515 ** 
median_income:total_rooms                                   1.434e+01  7.056e+00   2.032 0.042131 *  
median_income:latitude                                     -1.654e-01  5.967e-01  -0.277 0.781604    
median_income:longitude                                    -5.561e-01  2.276e-01  -2.443 0.014567 *  
median_income:total_bedrooms                               -1.008e+01  8.116e+00  -1.242 0.214176    
median_income:housing_median_age                            1.052e+00  1.755e+00   0.600 0.548818    
median_income:beds_per_rooms                               -1.327e+00  4.698e+00  -0.282 0.777573    
median_income:rooms_per_capita                             -1.204e+01  6.316e+00  -1.906 0.056657 .  
median_income:rooms_per_household                           9.921e+00  3.982e+00   2.492 0.012734 *  
median_income:population                                   -6.461e-01  5.542e+00  -0.117 0.907186    
median_income:income_per_capita                             4.459e+00  1.324e+00   3.368 0.000760 ***
enc_ocean_proximity:total_rooms                            -7.476e+00  7.653e+00  -0.977 0.328650    
enc_ocean_proximity:latitude                                4.188e+00  3.585e-01  11.681  < 2e-16 ***
enc_ocean_proximity:longitude                              -1.195e+00  9.944e-02 -12.016  < 2e-16 ***
enc_ocean_proximity:total_bedrooms                         -2.608e+00  8.025e+00  -0.325 0.745250    
enc_ocean_proximity:housing_median_age                     -1.639e+01  1.426e+00 -11.497  < 2e-16 ***
enc_ocean_proximity:beds_per_rooms                          3.522e+00  3.014e+00   1.169 0.242571    
enc_ocean_proximity:rooms_per_capita                       -1.081e+01  4.084e+00  -2.648 0.008115 ** 
enc_ocean_proximity:rooms_per_household                     1.769e+01  4.706e+00   3.758 0.000172 ***
enc_ocean_proximity:population                              6.362e-01  4.934e+00   0.129 0.897412    
enc_ocean_proximity:income_per_capita                      -1.526e+00  3.607e+00  -0.423 0.672182    
total_rooms:latitude                                        2.122e+00  2.040e+00   1.040 0.298286    
total_rooms:longitude                                      -1.210e+00  6.830e-01  -1.772 0.076456 .  
total_rooms:total_bedrooms                                 -6.950e+00  1.945e+00  -3.574 0.000353 ***
total_rooms:housing_median_age                             -1.159e+01  7.707e+00  -1.504 0.132483    
total_rooms:beds_per_rooms                                         NA         NA      NA       NA    
total_rooms:rooms_per_capita                               -6.342e+00  1.538e+01  -0.413 0.679980    
total_rooms:rooms_per_household                            -8.460e+00  1.444e+01  -0.586 0.558013    
total_rooms:population                                     -2.847e+00  2.969e+00  -0.959 0.337599    
total_rooms:income_per_capita                                      NA         NA      NA       NA    
latitude:longitude                                          1.873e-02  3.306e-03   5.667 1.49e-08 ***
latitude:total_bedrooms                                     6.886e-01  2.084e+00   0.330 0.741095    
latitude:housing_median_age                                -2.527e+00  3.600e-01  -7.019 2.37e-12 ***
latitude:beds_per_rooms                                     2.372e+00  5.890e-01   4.028 5.67e-05 ***
latitude:rooms_per_capita                                  -2.022e+00  1.018e+00  -1.986 0.047034 *  
latitude:rooms_per_household                                2.110e+00  9.314e-01   2.266 0.023487 *  
latitude:population                                        -3.335e+00  1.428e+00  -2.335 0.019575 *  
latitude:income_per_capita                                  2.017e+00  1.742e+00   1.158 0.246933    
longitude:total_bedrooms                                    4.055e-01  8.116e-01   0.500 0.617399    
longitude:housing_median_age                                3.993e-01  9.782e-02   4.081 4.51e-05 ***
longitude:beds_per_rooms                                   -1.006e+00  2.384e-01  -4.221 2.45e-05 ***
longitude:rooms_per_capita                                  3.100e-01  3.017e-01   1.028 0.304120    
longitude:rooms_per_household                              -2.634e-01  2.598e-01  -1.014 0.310512    
longitude:population                                        1.039e+00  3.904e-01   2.662 0.007790 ** 
longitude:income_per_capita                                 4.930e-01  1.730e+00   0.285 0.775643    
total_bedrooms:housing_median_age                          -7.772e+00  7.976e+00  -0.974 0.329906    
total_bedrooms:beds_per_rooms                              -6.599e+00  7.408e+00  -0.891 0.373060    
total_bedrooms:rooms_per_capita                             1.446e+01  1.451e+01   0.996 0.319135    
total_bedrooms:rooms_per_household                          1.968e+00  1.308e+01   0.150 0.880378    
total_bedrooms:population                                   9.064e+00  3.135e+00   2.891 0.003844 ** 
total_bedrooms:income_per_capita                            6.266e+01  1.172e+02   0.535 0.592745    
housing_median_age:beds_per_rooms                           5.256e+00  2.270e+00   2.315 0.020625 *  
housing_median_age:rooms_per_capita                         1.333e+01  3.452e+00   3.862 0.000113 ***
housing_median_age:rooms_per_household                     -5.394e+00  3.211e+00  -1.680 0.093025 .  
housing_median_age:population                               1.915e+01  5.212e+00   3.675 0.000239 ***
housing_median_age:income_per_capita                        1.850e+00  2.798e+00   0.661 0.508576    
beds_per_rooms:rooms_per_capita                            -1.639e+01  5.072e+00  -3.231 0.001236 ** 
beds_per_rooms:rooms_per_household                          7.677e+00  4.453e+00   1.724 0.084766 .  
beds_per_rooms:population                                  -9.446e+00  7.160e+00  -1.319 0.187120    
beds_per_rooms:income_per_capita                            7.413e+00  2.190e+00   3.385 0.000715 ***
rooms_per_capita:rooms_per_household                        2.688e-02  7.693e-01   0.035 0.972126    
rooms_per_capita:population                                        NA         NA      NA       NA    
rooms_per_capita:income_per_capita                          7.706e+00  2.742e+00   2.810 0.004961 ** 
rooms_per_household:population                              1.176e-01  6.103e+00   0.019 0.984621    
rooms_per_household:income_per_capita                      -3.660e+00  3.173e+00  -1.153 0.248768    
population:income_per_capita                                       NA         NA      NA       NA    
median_income:enc_ocean_proximity:total_rooms               1.831e-01  5.791e-02   3.161 0.001574 ** 
median_income:enc_ocean_proximity:latitude                 -3.957e-02  2.600e-02  -1.522 0.128016    
median_income:enc_ocean_proximity:longitude                -6.383e-02  2.624e-02  -2.432 0.015016 *  
median_income:enc_ocean_proximity:total_bedrooms           -4.896e-02  7.023e-02  -0.697 0.485683    
median_income:enc_ocean_proximity:housing_median_age       -2.709e-02  1.279e-02  -2.117 0.034282 *  
median_income:enc_ocean_proximity:beds_per_rooms           -1.560e-02  4.328e-02  -0.360 0.718596    
median_income:enc_ocean_proximity:rooms_per_capita         -1.198e-01  5.977e-02  -2.005 0.044995 *  
median_income:enc_ocean_proximity:rooms_per_household       3.157e-02  3.505e-02   0.901 0.367753    
median_income:enc_ocean_proximity:population               -1.590e-01  5.846e-02  -2.720 0.006541 ** 
median_income:enc_ocean_proximity:income_per_capita         3.206e-02  1.115e-02   2.876 0.004035 ** 
median_income:total_rooms:latitude                          2.071e-01  7.978e-02   2.596 0.009453 ** 
median_income:total_rooms:longitude                         1.944e-01  8.126e-02   2.392 0.016754 *  
median_income:total_rooms:total_bedrooms                   -8.605e-02  2.104e-02  -4.090 4.35e-05 ***
median_income:total_rooms:housing_median_age               -2.954e-01  4.917e-02  -6.008 1.94e-09 ***
median_income:total_rooms:beds_per_rooms                           NA         NA      NA       NA    
median_income:total_rooms:rooms_per_capita                 -4.392e-02  9.322e-02  -0.471 0.637511    
median_income:total_rooms:rooms_per_household               1.411e-02  8.133e-02   0.174 0.862238    
median_income:total_rooms:population                        5.662e-03  2.150e-02   0.263 0.792318    
median_income:total_rooms:income_per_capita                -1.793e+00  2.384e-01  -7.521 5.85e-14 ***
median_income:latitude:longitude                            2.578e-03  4.788e-03   0.538 0.590300    
median_income:latitude:total_bedrooms                      -1.556e-01  9.201e-02  -1.692 0.090750 .  
median_income:latitude:housing_median_age                  -1.243e-02  1.854e-02  -0.671 0.502378    
median_income:latitude:beds_per_rooms                      -1.582e-02  5.080e-02  -0.311 0.755548    
median_income:latitude:rooms_per_capita                    -1.861e-01  6.839e-02  -2.721 0.006524 ** 
median_income:latitude:rooms_per_household                  1.355e-01  4.195e-02   3.230 0.001241 ** 
median_income:latitude:population                          -5.546e-02  6.387e-02  -0.868 0.385182    
median_income:latitude:income_per_capita                    5.887e-02  1.597e-02   3.686 0.000229 ***
median_income:longitude:total_bedrooms                     -1.392e-01  9.343e-02  -1.490 0.136356    
median_income:longitude:housing_median_age                  5.563e-03  1.984e-02   0.280 0.779141    
median_income:longitude:beds_per_rooms                     -1.368e-02  5.350e-02  -0.256 0.798177    
median_income:longitude:rooms_per_capita                   -1.621e-01  7.197e-02  -2.252 0.024341 *  
median_income:longitude:rooms_per_household                 1.245e-01  4.495e-02   2.770 0.005615 ** 
median_income:longitude:population                         -2.628e-02  6.391e-02  -0.411 0.680864    
median_income:longitude:income_per_capita                   5.742e-02  1.521e-02   3.774 0.000161 ***
median_income:total_bedrooms:housing_median_age             1.743e-01  5.787e-02   3.013 0.002595 ** 
median_income:total_bedrooms:beds_per_rooms                -9.119e-02  4.998e-02  -1.825 0.068087 .  
median_income:total_bedrooms:rooms_per_capita               1.483e-01  9.419e-02   1.575 0.115297    
median_income:total_bedrooms:rooms_per_household           -1.375e-01  8.099e-02  -1.698 0.089617 .  
median_income:total_bedrooms:population                     5.588e-02  3.113e-02   1.795 0.072687 .  
median_income:total_bedrooms:income_per_capita             -9.635e-02  2.719e-01  -0.354 0.723122    
median_income:housing_median_age:beds_per_rooms            -3.128e-02  2.443e-02  -1.280 0.200470    
median_income:housing_median_age:rooms_per_capita           9.968e-03  3.711e-02   0.269 0.788208    
median_income:housing_median_age:rooms_per_household       -7.985e-03  2.056e-02  -0.388 0.697792    
median_income:housing_median_age:population                 1.679e-01  4.631e-02   3.626 0.000289 ***
median_income:housing_median_age:income_per_capita          3.775e-03  9.212e-03   0.410 0.681946    
median_income:beds_per_rooms:rooms_per_capita                      NA         NA      NA       NA    
median_income:beds_per_rooms:rooms_per_household           -7.502e-02  3.808e-02  -1.970 0.048861 *  
median_income:beds_per_rooms:population                    -6.240e-02  5.394e-02  -1.157 0.247397    
median_income:beds_per_rooms:income_per_capita             -1.471e-02  1.134e-02  -1.297 0.194632    
median_income:rooms_per_capita:rooms_per_household         -1.459e-02  3.885e-02  -0.376 0.707223    
median_income:rooms_per_capita:population                          NA         NA      NA       NA    
median_income:rooms_per_capita:income_per_capita           -2.865e-03  1.531e-02  -0.187 0.851603    
median_income:rooms_per_household:population                2.244e-01  7.396e-02   3.034 0.002421 ** 
median_income:rooms_per_household:income_per_capita         2.631e-02  1.570e-02   1.676 0.093791 .  
median_income:population:income_per_capita                  1.615e+00  3.069e-01   5.264 1.44e-07 ***
enc_ocean_proximity:total_rooms:latitude                   -9.730e-02  8.951e-02  -1.087 0.277046    
enc_ocean_proximity:total_rooms:longitude                  -9.195e-02  8.966e-02  -1.026 0.305129    
enc_ocean_proximity:total_rooms:total_bedrooms              1.164e-02  2.264e-02   0.514 0.607095    
enc_ocean_proximity:total_rooms:housing_median_age          7.723e-02  5.528e-02   1.397 0.162401    
enc_ocean_proximity:total_rooms:beds_per_rooms                     NA         NA      NA       NA    
enc_ocean_proximity:total_rooms:rooms_per_capita           -3.324e-01  1.344e-01  -2.474 0.013386 *  
enc_ocean_proximity:total_rooms:rooms_per_household         1.892e-01  1.249e-01   1.514 0.130014    
enc_ocean_proximity:total_rooms:population                 -1.688e-02  2.461e-02  -0.686 0.492731    
enc_ocean_proximity:total_rooms:income_per_capita                  NA         NA      NA       NA    
enc_ocean_proximity:latitude:longitude                      3.453e-02  2.931e-03  11.783  < 2e-16 ***
enc_ocean_proximity:latitude:total_bedrooms                -2.625e-02  9.187e-02  -0.286 0.775045    
enc_ocean_proximity:latitude:housing_median_age            -1.571e-01  1.616e-02  -9.725  < 2e-16 ***
enc_ocean_proximity:latitude:beds_per_rooms                 4.423e-02  3.392e-02   1.304 0.192282    
enc_ocean_proximity:latitude:rooms_per_capita              -1.268e-01  4.740e-02  -2.676 0.007462 ** 
enc_ocean_proximity:latitude:rooms_per_household            1.466e-01  5.437e-02   2.697 0.007011 ** 
enc_ocean_proximity:latitude:population                     2.577e-02  5.722e-02   0.450 0.652379    
enc_ocean_proximity:latitude:income_per_capita             -6.554e-03  3.932e-02  -0.167 0.867625    
enc_ocean_proximity:longitude:total_bedrooms               -3.134e-02  9.341e-02  -0.336 0.737235    
enc_ocean_proximity:longitude:housing_median_age           -1.826e-01  1.649e-02 -11.075  < 2e-16 ***
enc_ocean_proximity:longitude:beds_per_rooms                4.306e-02  3.484e-02   1.236 0.216468    
enc_ocean_proximity:longitude:rooms_per_capita             -1.266e-01  4.762e-02  -2.658 0.007870 ** 
enc_ocean_proximity:longitude:rooms_per_household           1.902e-01  5.478e-02   3.472 0.000519 ***
enc_ocean_proximity:longitude:population                    1.457e-02  5.727e-02   0.254 0.799162    
enc_ocean_proximity:longitude:income_per_capita            -2.042e-02  3.899e-02  -0.524 0.600510    
enc_ocean_proximity:total_bedrooms:housing_median_age      -1.844e-01  5.406e-02  -3.412 0.000647 ***
enc_ocean_proximity:total_bedrooms:beds_per_rooms          -3.739e-02  5.657e-02  -0.661 0.508707    
enc_ocean_proximity:total_bedrooms:rooms_per_capita         1.673e-01  1.185e-01   1.412 0.158114    
enc_ocean_proximity:total_bedrooms:rooms_per_household     -9.523e-02  1.092e-01  -0.872 0.383203    
enc_ocean_proximity:total_bedrooms:population               1.317e-02  2.692e-02   0.489 0.624688    
enc_ocean_proximity:total_bedrooms:income_per_capita        5.485e-01  1.157e+00   0.474 0.635343    
enc_ocean_proximity:housing_median_age:beds_per_rooms       2.571e-02  1.747e-02   1.472 0.141181    
enc_ocean_proximity:housing_median_age:rooms_per_capita     9.973e-02  2.612e-02   3.819 0.000135 ***
enc_ocean_proximity:housing_median_age:rooms_per_household -7.646e-02  2.806e-02  -2.725 0.006441 ** 
enc_ocean_proximity:housing_median_age:population           1.334e-01  4.170e-02   3.198 0.001387 ** 
enc_ocean_proximity:housing_median_age:income_per_capita    8.395e-03  1.891e-02   0.444 0.657159    
enc_ocean_proximity:beds_per_rooms:rooms_per_capita        -1.868e-01  4.172e-02  -4.479 7.59e-06 ***
enc_ocean_proximity:beds_per_rooms:rooms_per_household      1.241e-01  3.582e-02   3.466 0.000530 ***
enc_ocean_proximity:beds_per_rooms:population              -1.556e-01  6.289e-02  -2.474 0.013374 *  
enc_ocean_proximity:beds_per_rooms:income_per_capita        1.754e-02  2.353e-02   0.745 0.456022    
enc_ocean_proximity:rooms_per_capita:rooms_per_household   -8.721e-03  1.192e-02  -0.731 0.464547    
enc_ocean_proximity:rooms_per_capita:population                    NA         NA      NA       NA    
enc_ocean_proximity:rooms_per_capita:income_per_capita      3.542e-02  2.547e-02   1.391 0.164305    
enc_ocean_proximity:rooms_per_household:population         -2.137e-01  8.805e-02  -2.427 0.015230 *  
enc_ocean_proximity:rooms_per_household:income_per_capita  -6.637e-03  3.216e-02  -0.206 0.836486    
enc_ocean_proximity:population:income_per_capita                   NA         NA      NA       NA    
total_rooms:latitude:longitude                              1.974e-02  1.675e-02   1.179 0.238419    
total_rooms:latitude:total_bedrooms                        -7.009e-02  2.277e-02  -3.079 0.002084 ** 
total_rooms:latitude:housing_median_age                    -8.948e-02  8.389e-02  -1.067 0.286150    
total_rooms:latitude:beds_per_rooms                                NA         NA      NA       NA    
total_rooms:latitude:rooms_per_capita                      -1.609e-01  1.540e-01  -1.045 0.296170    
total_rooms:latitude:rooms_per_household                   -8.954e-02  1.422e-01  -0.630 0.528813    
total_rooms:latitude:population                            -3.898e-02  3.414e-02  -1.142 0.253552    
total_rooms:latitude:income_per_capita                             NA         NA      NA       NA    
total_rooms:longitude:total_bedrooms                       -7.547e-02  2.230e-02  -3.384 0.000717 ***
total_rooms:longitude:housing_median_age                   -1.196e-01  8.831e-02  -1.355 0.175475    
total_rooms:longitude:beds_per_rooms                               NA         NA      NA       NA    
total_rooms:longitude:rooms_per_capita                     -1.013e-01  1.718e-01  -0.590 0.555384    
total_rooms:longitude:rooms_per_household                  -1.031e-01  1.610e-01  -0.641 0.521691    
total_rooms:longitude:population                           -3.893e-02  3.458e-02  -1.126 0.260355    
total_rooms:longitude:income_per_capita                            NA         NA      NA       NA    
total_rooms:total_bedrooms:housing_median_age              -3.397e-02  1.699e-02  -1.999 0.045624 *  
total_rooms:total_bedrooms:beds_per_rooms                   8.571e-02  3.871e-02   2.214 0.026829 *  
total_rooms:total_bedrooms:rooms_per_capita                -2.112e-02  1.362e-02  -1.551 0.120938    
total_rooms:total_bedrooms:rooms_per_household              4.324e-02  1.876e-02   2.305 0.021212 *  
total_rooms:total_bedrooms:population                       7.581e-04  6.264e-04   1.210 0.226163    
total_rooms:total_bedrooms:income_per_capita                       NA         NA      NA       NA    
 [ reached getOption("max.print") -- omitted 99 rows ]
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5599 on 11292 degrees of freedom
Multiple R-squared:  0.7729,    Adjusted R-squared:  0.7677 
F-statistic: 147.2 on 261 and 11292 DF,  p-value: < 2.2e-16

scores(full_threeway_model, xs=validate1, y=validate1$median_house_value)

prediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleading

Entrenamiento de modelos robustos (tolerantes a outliers)

MM-type regression

fitLmrob<-lmrob(median_house_value ~ median_income+poly(median_income, 2) +
                                latitude * longitude +
                                enc_ocean_proximity +
                                population+poly(population, 2)+
                                total_rooms*total_bedrooms+
                                total_bedrooms+poly(total_bedrooms, 3)+
                                housing_median_age+poly(housing_median_age, 3)+
                                beds_per_rooms+poly(beds_per_rooms, 3)+
                                rooms_per_capita+
                                rooms_per_household+poly(rooms_per_household, 3)+
                                income_per_capita
                                , data = extractTrainingVars(train1))

summary(fitLmrob)
scores(fitLmrob, xs=validate1, y=validate1$median_house_value, cost=rtmspe, trim=0.1)

LTS robust regression

fitLts<-ltsReg(median_house_value ~ median_income+poly(median_income, 2) +
                                latitude * longitude +
                                enc_ocean_proximity +
                                population+poly(population, 2)+
                                total_rooms*total_bedrooms+
                                total_bedrooms+poly(total_bedrooms, 3)+
                                housing_median_age+poly(housing_median_age, 3)+
                                beds_per_rooms+poly(beds_per_rooms, 3)+
                                rooms_per_capita+
                                rooms_per_household+poly(rooms_per_household, 3)+
                                income_per_capita
                                , data = extractTrainingVars(train1))
print("fitted")
scores(fitLts, cost=rtmspe, trim=0.1)

irls<-rlm(median_house_value ~ median_income+poly(median_income, 2) +
                                latitude * longitude +
                                enc_ocean_proximity +
                                population+poly(population, 2)+
                                total_rooms*total_bedrooms+
                                total_bedrooms+poly(total_bedrooms, 3)+
                                housing_median_age+poly(housing_median_age, 3)+
                                beds_per_rooms+poly(beds_per_rooms, 3)+
                                rooms_per_capita+
                                rooms_per_household+poly(rooms_per_household, 3)+
                                income_per_capita
                                , data = extractTrainingVars(train1))
irls_bi<-rlm(median_house_value ~median_income+poly(median_income, 2) +
                                latitude * longitude +
                                enc_ocean_proximity +
                                population+poly(population, 2)+
                                total_rooms*total_bedrooms+
                                total_bedrooms+poly(total_bedrooms, 3)+
                                housing_median_age+poly(housing_median_age, 3)+
                                beds_per_rooms+poly(beds_per_rooms, 3)+
                                rooms_per_capita+
                                rooms_per_household+poly(rooms_per_household, 3)+
                                income_per_capita
                                , data = extractTrainingVars(train1), psi = psi.bisquare)
summary(irls)
summary(irls_bi)

scores(irls, xs=validate1, y=validate1$median_house_value)
scores(irls_bi,  xs=validate1, y=validate1$median_house_value)

Predicciones en test-set

timestamp<-function() {
  my_options <- options(digits.secs = 3)
  timestamp<-strftime(Sys.time(), "%m%d_%H%M%OS")
  options(my_options)  
  return(timestamp)
}

writePredictions<-function(predictions, name, ids=testing_set$id) {
  data<-cbind(id=ids, median_house_value=abs(predictions*median_house_value_scale))
  filename<-paste("predictions/", timestamp(), "_", name, ".csv", sep="")
  write.csv(data, filename, row.names = FALSE, quote=FALSE)
}

writePredictions1<-function(model, name, test_set=testing_set) {
  writePredictions(predict(model, test_set), name)
}

testing_set<-loadAndPreprocess("test.csv")

coded 1 cols 5 levels 

testing_set<-imp_total_bedrooms(testing_set)
testing_set<-addExtraFeats(testing_set)
testing_set<-predict(preProcess1, testing_set)

#writePredictions1(fitLmrob, "fitLmrob")
#writePredictions1(fitLts, "fitLts")
#writePredictions1(irls, "irls")
writePredictions1(full_threeway_model, "full_threeway_model")

Clustering

Cálculo de matriz de distancias

x <- train1$longitude
y <- train1$latitude

xy <- SpatialPointsDataFrame(
      matrix(c(x,y), ncol=2), data.frame(ID=train1$id),
      proj4string=CRS("+proj=longlat +ellps=WGS84 +datum=WGS84"))

mdist <- distm(xy)

Dividir training set en clusters

hc <- hclust(as.dist(mdist), method="complete")

d=40000 # radio en metros

xy$clust <- cutree(hc, h=d)
train1$clust <- factor(xy$clust)

Calcular el centroide de cada cluster

cent <- matrix(ncol=2, nrow=max(xy$clust))
for (i in 1:max(xy$clust))
    cent[i,] <- gCentroid(subset(xy, clust == i))@coords

Visualización

xy@bbox[] <- as.matrix(extend(extent(xy),0.001))

ci <- circles(cent, d=d, lonlat=T)

plot(ci@polygons, axes=T)
plot(xy, col=rainbow(max(xy$clust))[factor(xy$clust)], add=T)

as.data.frame(table(xy$clust))

points<-data.frame(x=validate1$longitude, y=validate1$latitude)
validate1$clust<-factor(nn2(as.data.frame(cent), query=points,k=1)$nn.idx)

points<-data.frame(x=testing_set$longitude, y=testing_set$latitude)
testing_set$clust<-factor(nn2(as.data.frame(cent), query=points,k=1)$nn.idx)

OHE_clust<-function(df) {
  col<-df %>% dplyr::select(clust)
  encoder<-dummyVars("~.", data=col, x=factor(1:240))
  cols<-data.frame(predict(encoder, newdata = col))
  return(cbind(df, cols))
}

trainClust<-OHE_clust(train1)
validateClust<-OHE_clust(validate1)
testing_setClust<-OHE_clust(testing_set)

extractTrainingVarsClust<-function(data) {
  return(data %>% dplyr::select(median_house_value, 
                median_income,
                enc_ocean_proximity,
                total_rooms,
                latitude,
                longitude,
                total_bedrooms,
                housing_median_age,
                beds_per_rooms,
                rooms_per_capita,
                rooms_per_household,
                population,
                income_per_capita, starts_with("clust.")))
}

fitClust<-lm(median_house_value ~ median_income+poly(median_income, 2) +
                                latitude * longitude +
                                enc_ocean_proximity +
                                population+poly(population, 2)+
                                total_rooms*total_bedrooms+
                                total_bedrooms+poly(total_bedrooms, 3)+
                                housing_median_age+poly(housing_median_age, 3)+
                                beds_per_rooms+poly(beds_per_rooms, 3)+
                                rooms_per_capita+
                                rooms_per_household+poly(rooms_per_household, 3)+
                                income_per_capita + .
                                , data = extractTrainingVarsClust(trainClust))

summary(fitClust)

Call:
lm(formula = median_house_value ~ median_income + poly(median_income, 
    2) + latitude * longitude + enc_ocean_proximity + population + 
    poly(population, 2) + total_rooms * total_bedrooms + total_bedrooms + 
    poly(total_bedrooms, 3) + housing_median_age + poly(housing_median_age, 
    3) + beds_per_rooms + poly(beds_per_rooms, 3) + rooms_per_capita + 
    rooms_per_household + poly(rooms_per_household, 3) + income_per_capita + 
    ., data = extractTrainingVarsClust(trainClust))

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2312 -0.3147 -0.0533  0.2416  4.3074 

Coefficients: (7 not defined because of singularities)
                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                   -1.009e+03  1.168e+02  -8.635  < 2e-16 ***
median_income                  5.628e-01  1.158e-02  48.599  < 2e-16 ***
poly(median_income, 2)1               NA         NA      NA       NA    
poly(median_income, 2)2       -3.712e+00  6.710e-01  -5.533 3.23e-08 ***
latitude                       2.419e+01  3.269e+00   7.398 1.48e-13 ***
longitude                     -8.695e+00  9.777e-01  -8.894  < 2e-16 ***
enc_ocean_proximity            6.237e-02  1.566e-02   3.984 6.83e-05 ***
population                    -4.089e-02  1.941e-02  -2.107 0.035178 *  
poly(population, 2)1                  NA         NA      NA       NA    
poly(population, 2)2           3.321e+00  1.078e+00   3.080 0.002072 ** 
total_rooms                    5.720e-02  3.954e-02   1.446 0.148078    
total_bedrooms                 3.076e-02  2.777e-02   1.108 0.267898    
poly(total_bedrooms, 3)1              NA         NA      NA       NA    
poly(total_bedrooms, 3)2      -1.772e+00  2.720e+00  -0.651 0.514815    
poly(total_bedrooms, 3)3       6.853e-02  6.591e-01   0.104 0.917191    
housing_median_age             4.232e-02  7.385e-03   5.730 1.03e-08 ***
poly(housing_median_age, 3)1          NA         NA      NA       NA    
poly(housing_median_age, 3)2   1.660e+00  6.358e-01   2.610 0.009066 ** 
poly(housing_median_age, 3)3   2.747e+00  6.073e-01   4.523 6.17e-06 ***
beds_per_rooms                 7.938e-02  1.690e-02   4.696 2.68e-06 ***
poly(beds_per_rooms, 3)1              NA         NA      NA       NA    
poly(beds_per_rooms, 3)2       3.166e+00  8.885e-01   3.564 0.000367 ***
poly(beds_per_rooms, 3)3      -6.293e+00  6.797e-01  -9.257  < 2e-16 ***
rooms_per_capita               4.735e-01  1.768e-02  26.774  < 2e-16 ***
rooms_per_household           -2.678e-01  1.686e-02 -15.882  < 2e-16 ***
poly(rooms_per_household, 3)1         NA         NA      NA       NA    
poly(rooms_per_household, 3)2 -1.193e+01  1.035e+00 -11.532  < 2e-16 ***
poly(rooms_per_household, 3)3  5.879e+00  8.168e-01   7.198 6.49e-13 ***
income_per_capita             -1.210e-02  5.876e-03  -2.059 0.039503 *  
clust.1                       -4.019e+00  8.911e-01  -4.510 6.54e-06 ***
clust.2                       -2.734e+00  9.067e-01  -3.016 0.002569 ** 
clust.3                       -2.966e+00  9.042e-01  -3.280 0.001040 ** 
clust.4                       -1.394e+00  6.382e-01  -2.184 0.028987 *  
clust.5                       -1.354e+00  6.272e-01  -2.159 0.030898 *  
clust.6                       -1.569e+00  6.656e-01  -2.357 0.018418 *  
clust.7                       -3.172e+00  8.493e-01  -3.735 0.000189 ***
clust.8                       -1.626e+00  6.555e-01  -2.481 0.013103 *  
clust.9                       -3.677e+00  8.945e-01  -4.110 3.98e-05 ***
clust.10                      -3.546e+00  8.765e-01  -4.046 5.25e-05 ***
clust.11                      -3.163e+00  8.985e-01  -3.520 0.000433 ***
clust.12                      -2.039e+00  6.587e-01  -3.095 0.001972 ** 
clust.13                      -8.955e-01  1.107e+00  -0.809 0.418699    
clust.14                      -8.430e-01  1.038e+00  -0.812 0.416790    
clust.15                      -1.642e+00  9.695e-01  -1.693 0.090458 .  
clust.16                      -2.787e+00  9.279e-01  -3.004 0.002674 ** 
clust.17                      -1.150e+00  1.148e+00  -1.001 0.316750    
clust.18                       3.336e+00  6.211e-01   5.371 7.97e-08 ***
clust.19                      -3.409e+00  7.702e-01  -4.426 9.68e-06 ***
clust.20                      -1.088e+00  1.031e+00  -1.055 0.291231    
clust.21                      -1.554e+00  6.669e-01  -2.330 0.019799 *  
clust.22                      -1.783e+00  9.399e-01  -1.897 0.057913 .  
clust.23                      -3.388e+00  9.353e-01  -3.622 0.000293 ***
clust.24                      -8.905e-01  5.886e-01  -1.513 0.130345    
clust.25                      -1.861e+00  6.484e-01  -2.870 0.004107 ** 
clust.26                      -1.551e+00  6.436e-01  -2.410 0.015972 *  
clust.27                      -3.340e+00  7.138e-01  -4.679 2.92e-06 ***
clust.28                      -3.154e+00  8.862e-01  -3.559 0.000374 ***
clust.29                      -2.911e+00  7.720e-01  -3.770 0.000164 ***
clust.30                      -3.209e+00  8.042e-01  -3.991 6.62e-05 ***
clust.31                      -6.069e-01  5.933e-01  -1.023 0.306405    
clust.32                      -8.021e-01  6.168e-01  -1.300 0.193473    
clust.33                      -1.715e+00  9.382e-01  -1.828 0.067582 .  
clust.34                      -3.424e+00  7.371e-01  -4.645 3.44e-06 ***
clust.35                      -3.327e+00  9.184e-01  -3.622 0.000294 ***
clust.36                      -2.015e+00  6.756e-01  -2.982 0.002867 ** 
clust.37                      -3.883e+00  9.009e-01  -4.311 1.64e-05 ***
clust.38                      -3.851e+00  7.781e-01  -4.949 7.56e-07 ***
clust.39                      -1.838e+00  9.768e-01  -1.882 0.059913 .  
clust.40                      -1.476e+00  6.444e-01  -2.291 0.021986 *  
clust.41                      -3.650e+00  8.928e-01  -4.089 4.37e-05 ***
clust.42                      -3.111e+00  7.833e-01  -3.972 7.17e-05 ***
clust.43                      -3.403e+00  8.094e-01  -4.204 2.64e-05 ***
clust.44                      -1.299e+00  6.359e-01  -2.042 0.041140 *  
clust.45                      -4.589e+00  8.146e-01  -5.634 1.81e-08 ***
clust.46                      -3.542e+00  9.098e-01  -3.893 9.97e-05 ***
clust.47                      -3.051e+00  8.603e-01  -3.547 0.000392 ***
clust.48                      -1.332e+00  6.355e-01  -2.096 0.036122 *  
clust.49                      -3.988e+00  8.642e-01  -4.615 3.98e-06 ***
clust.50                      -2.170e+00  9.165e-01  -2.368 0.017918 *  
clust.51                      -1.012e+00  6.057e-01  -1.671 0.094841 .  
clust.52                      -6.876e-01  1.050e+00  -0.655 0.512555    
clust.53                      -6.675e-01  5.967e-01  -1.119 0.263317    
clust.54                      -1.655e+00  6.538e-01  -2.531 0.011383 *  
clust.55                      -3.499e+00  9.277e-01  -3.771 0.000163 ***
clust.56                       1.007e-01  1.293e+00   0.078 0.937910    
clust.57                      -2.730e+00  9.819e-01  -2.781 0.005430 ** 
clust.58                      -3.274e+00  9.187e-01  -3.564 0.000367 ***
clust.59                      -3.540e+00  7.953e-01  -4.451 8.63e-06 ***
clust.60                      -3.181e+00  9.102e-01  -3.495 0.000475 ***
clust.61                      -1.230e+00  6.299e-01  -1.952 0.050911 .  
clust.62                      -1.473e+00  1.014e+00  -1.453 0.146288    
clust.63                      -2.887e+00  7.865e-01  -3.671 0.000243 ***
clust.64                      -1.741e+00  1.000e+00  -1.740 0.081834 .  
clust.65                      -2.510e+00  9.173e-01  -2.736 0.006229 ** 
clust.66                      -2.734e-01  6.099e-01  -0.448 0.653998    
clust.67                      -2.142e+00  9.525e-01  -2.248 0.024570 *  
clust.68                      -2.187e+00  6.835e-01  -3.199 0.001381 ** 
clust.69                      -3.710e+00  8.703e-01  -4.263 2.04e-05 ***
clust.70                      -3.190e+00  7.082e-01  -4.505 6.71e-06 ***
clust.71                      -2.709e+00  9.509e-01  -2.848 0.004401 ** 
clust.72                       4.068e-01  6.029e-01   0.675 0.499824    
clust.73                      -3.473e+00  8.846e-01  -3.926 8.67e-05 ***
clust.74                      -1.460e+00  9.862e-01  -1.481 0.138662    
clust.75                      -2.591e+00  8.717e-01  -2.973 0.002956 ** 
clust.76                      -1.281e+00  9.868e-01  -1.299 0.194094    
clust.77                      -2.780e+00  6.946e-01  -4.002 6.33e-05 ***
clust.78                      -2.683e+00  9.605e-01  -2.793 0.005224 ** 
clust.79                      -3.325e+00  8.805e-01  -3.776 0.000160 ***
clust.80                       1.727e+00  5.904e-01   2.925 0.003454 ** 
clust.81                      -2.996e+00  9.940e-01  -3.014 0.002588 ** 
clust.82                      -3.777e+00  8.534e-01  -4.426 9.69e-06 ***
clust.83                      -3.384e+00  8.693e-01  -3.893 9.98e-05 ***
clust.84                      -2.752e+00  7.988e-01  -3.445 0.000573 ***
clust.85                      -3.200e+00  8.111e-01  -3.945 8.02e-05 ***
clust.86                      -7.728e-01  1.010e+00  -0.765 0.444297    
clust.87                      -4.642e+00  8.550e-01  -5.429 5.79e-08 ***
clust.88                      -4.374e+00  8.677e-01  -5.041 4.71e-07 ***
clust.89                      -3.402e+00  8.293e-01  -4.103 4.11e-05 ***
clust.90                      -1.716e+00  9.342e-01  -1.837 0.066214 .  
clust.91                      -3.299e+00  8.634e-01  -3.821 0.000133 ***
clust.92                      -9.330e-01  6.277e-01  -1.486 0.137189    
clust.93                      -1.975e+00  9.193e-01  -2.149 0.031679 *  
clust.94                      -3.025e+00  9.353e-01  -3.234 0.001224 ** 
clust.95                      -7.324e-01  5.941e-01  -1.233 0.217683    
clust.96                      -1.268e+00  6.400e-01  -1.982 0.047507 *  
clust.97                      -3.538e+00  9.593e-01  -3.688 0.000227 ***
clust.98                      -1.338e+00  1.041e+00  -1.285 0.198788    
clust.99                      -2.169e+00  9.838e-01  -2.204 0.027512 *  
clust.100                     -5.182e+00  7.810e-01  -6.635 3.39e-11 ***
clust.101                      1.716e+00  5.828e-01   2.944 0.003247 ** 
clust.102                     -2.482e+00  9.108e-01  -2.726 0.006429 ** 
clust.103                      4.337e-01  1.241e+00   0.349 0.726794    
clust.104                     -1.034e+00  6.791e-01  -1.522 0.127959    
clust.105                     -4.482e+00  8.356e-01  -5.364 8.29e-08 ***
clust.106                     -1.614e+00  8.825e-01  -1.829 0.067470 .  
clust.107                     -3.116e+00  8.054e-01  -3.869 0.000110 ***
clust.108                     -3.158e+00  9.782e-01  -3.229 0.001248 ** 
clust.109                     -2.112e+00  9.124e-01  -2.315 0.020622 *  
clust.110                     -2.466e+00  9.367e-01  -2.632 0.008488 ** 
clust.111                     -2.878e+00  7.535e-01  -3.819 0.000135 ***
clust.112                     -1.034e+00  6.273e-01  -1.648 0.099316 .  
clust.113                     -4.907e+00  8.143e-01  -6.026 1.74e-09 ***
clust.114                     -3.533e+00  8.299e-01  -4.258 2.08e-05 ***
clust.115                     -2.066e+00  7.322e-01  -2.821 0.004788 ** 
clust.116                     -4.269e+00  8.722e-01  -4.895 9.99e-07 ***
clust.117                     -2.283e-01  6.160e-01  -0.371 0.710919    
clust.118                     -3.955e+00  7.544e-01  -5.242 1.62e-07 ***
clust.119                     -2.852e+00  9.400e-01  -3.034 0.002420 ** 
clust.120                     -4.702e-01  1.205e+00  -0.390 0.696473    
clust.121                     -3.365e+00  8.461e-01  -3.977 7.03e-05 ***
clust.122                     -2.704e+00  6.954e-01  -3.889 0.000101 ***
clust.123                     -4.830e+00  8.503e-01  -5.681 1.37e-08 ***
clust.124                     -1.459e+00  8.686e-01  -1.680 0.092968 .  
clust.125                     -1.861e+00  7.069e-01  -2.632 0.008498 ** 
clust.126                     -4.450e+00  7.947e-01  -5.599 2.21e-08 ***
clust.127                     -3.595e+00  8.586e-01  -4.187 2.85e-05 ***
clust.128                     -3.741e+00  7.627e-01  -4.905 9.46e-07 ***
clust.129                     -2.388e+00  7.261e-01  -3.288 0.001011 ** 
clust.130                     -2.775e+00  7.548e-01  -3.676 0.000238 ***
clust.131                      4.702e-01  6.231e-01   0.755 0.450436    
clust.132                     -3.031e+00  9.964e-01  -3.042 0.002359 ** 
clust.133                     -1.135e+00  6.546e-01  -1.734 0.082968 .  
clust.134                     -5.511e+00  7.826e-01  -7.042 2.01e-12 ***
clust.135                     -3.053e+00  7.362e-01  -4.147 3.39e-05 ***
clust.136                     -5.060e+00  9.352e-01  -5.410 6.42e-08 ***
clust.137                     -3.428e+00  9.836e-01  -3.485 0.000494 ***
clust.138                     -3.300e+00  8.756e-01  -3.769 0.000164 ***
clust.139                     -1.617e+00  1.061e+00  -1.524 0.127467    
clust.140                     -2.823e+00  9.151e-01  -3.085 0.002037 ** 
clust.141                     -2.239e+00  6.934e-01  -3.229 0.001247 ** 
clust.142                      1.647e-01  6.725e-01   0.245 0.806492    
clust.143                     -3.270e+00  8.397e-01  -3.894 9.90e-05 ***
clust.144                      3.768e-01  8.332e-01   0.452 0.651101    
clust.145                     -3.317e+00  8.277e-01  -4.007 6.18e-05 ***
clust.146                     -2.219e+00  9.847e-01  -2.253 0.024259 *  
clust.147                     -3.174e+00  1.146e+00  -2.770 0.005607 ** 
clust.148                     -4.876e+00  8.288e-01  -5.883 4.15e-09 ***
clust.149                     -3.050e+00  8.945e-01  -3.410 0.000652 ***
clust.150                      4.130e-01  7.009e-01   0.589 0.555648    
clust.151                      2.994e-01  1.153e+00   0.260 0.795196    
clust.152                     -4.437e+00  8.571e-01  -5.177 2.29e-07 ***
clust.153                     -1.012e+00  1.104e+00  -0.917 0.359106    
clust.154                     -3.786e+00  8.756e-01  -4.324 1.55e-05 ***
clust.155                      2.016e-02  6.552e-01   0.031 0.975457    
clust.156                     -2.941e+00  9.463e-01  -3.108 0.001890 ** 
clust.157                     -8.405e-01  1.173e+00  -0.716 0.473725    
clust.158                     -3.383e-01  1.103e+00  -0.307 0.759089    
clust.159                     -2.839e+00  1.045e+00  -2.716 0.006616 ** 
clust.160                     -1.694e+00  7.884e-01  -2.149 0.031643 *  
clust.161                     -3.788e-01  6.499e-01  -0.583 0.560022    
clust.162                     -1.219e+00  1.091e+00  -1.118 0.263739    
clust.163                     -2.170e-01  6.214e-01  -0.349 0.726884    
clust.164                     -1.691e+00  6.928e-01  -2.441 0.014682 *  
clust.165                     -2.683e+00  7.731e-01  -3.470 0.000522 ***
clust.166                     -2.868e+00  8.597e-01  -3.336 0.000854 ***
clust.167                     -3.030e+00  1.074e+00  -2.821 0.004792 ** 
clust.168                     -3.771e+00  9.484e-01  -3.976 7.06e-05 ***
clust.169                     -3.037e+00  8.829e-01  -3.440 0.000584 ***
clust.170                     -3.089e+00  7.807e-01  -3.957 7.63e-05 ***
clust.171                      7.853e-01  1.270e+00   0.618 0.536523    
 [ reached getOption("max.print") -- omitted 71 rows ]
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5702 on 11290 degrees of freedom
Multiple R-squared:  0.7645,    Adjusted R-squared:  0.759 
F-statistic: 139.4 on 263 and 11290 DF,  p-value: < 2.2e-16

scores(fitClust, xs=validateClust, y=validateClust$median_house_value)

prediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleadingprediction from a rank-deficient fit may be misleading

writePredictions1(fitClust, "fitClust40km", test_set=testing_setClust)

prediction from a rank-deficient fit may be misleading